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Sylvester for his part ignored his hot-headed indiscretion - till
he got himself all steamed up for another. In many ways this
strangely congenial pair were like a honeymoon couple, except
that one party to the friendship never lost his temper. Although
Sylvester was Cayley's senior by seven years, we shall begin
with Cayley. Sylvester's life breaks naturally into the calm
stream of Cayley's like a jagged rock in the middle of a deep
Arthur Cayley was born on 16 August 1821 at Richmond,
Surrey, the second son of his parents, then residing temporarily
in England. On his father's side Cayley traced his descent back
to the days of the Norman Conquest (1066) and even before, to
a baronial estate in Normandy. The family was a talented one
which, like the Darwin family, should provide much suggestive
material for students of heredity. His mother was Maria
Antonia Doughty, by some said to have been of Russian origin.
Cayley's father was an English merchant engaged in the Rus-
sian trade; Arthur was born during one of the periodical visits
of his parents to England.
In 1829, when Arthur was eight, the merchant retired, to live
thenceforth in England. Arthur was sent to a private school at
Blackheath and later, at the age of fourteen, to King's College
School in London. His mathematical genius showed itself very
early. The first manifestations of superior talent were like those
of Gauss; young Cayley developed an amazing skill in long
numerical calculations which he undertook for amusement. On
beginning the formal study of mathematics he quickly out-
stripped the rest of the school. Presently he was in a class by
himself, as he was later when he went up to the University, and
his teachers agreed that the boy was a born mathematician
who should make mathematics his career. In grateful contrast
to Galois9 teachers, Cayley's recognized his ability from the
beginning and gave him every encouragement. At first the
retired merchant objected strongly to his son's becoming a
mathematician but finally, won over by the Principal of the
school, gave bis consent, his blessing, and his money. He
decided to send bis son to Cambridge.
Cayley began his university career at the age of seventeen at